Conditions for repulsive Casimir forces between identical birefringent materials

Abstract

Repulsive Casimir-Lifshitz forces are known to exist between two dissimilar materials if a third material, whose dielectric response is intermediate, separates them. However, the force between two identical materials is almost always attractive. Here we show that the force between two identical, semi-infinite birefringent slabs can be repulsive for particular orientations and compare the conditions for repulsion in this system to those of isotropic materials. We examine the dependence of the Casimir-Lifshitz force on retardation and relative orientation in this system and discuss situations in which the force can be changed from attractive to repulsive as a function of both distance and rotation angle.

Casimir-Lifshitz Torque Enhancement by Retardation and Intervening Dielectrics

“…where r and ϕ are the radial and azimuthal components of a wave vector, and D n (r, φ) = 0 represents the dispersion condition for surface modes between the slabs [4,22]. With substitution of the dimensionless χ = rd, the retarded Hamaker coefficient can be written as a sum of contributions at the Matsubara frequencies:…”

The Impact of the Anisotropy of the Media between Parallel Plates on the Casimir Force

“…Parashar and his colleagues calculated the Casimir force between two parallel semitransparent δ-function plates and between two parallel anisotropic dielectric slabs [16]. Somers and Munday found that, for particular orientations of optical axes, the Casimir force can be repulsive, even when the two anisotropic slabs are identical [17]. In recent years, scientists have started to investigate the interaction between anisotropic particles and a surface [16,18,19].…”

Repulsive vacuum-induced forces on a magnetic particle

“…(36), one can see from Eq. (44) and Eq. (B3) that in order to find the CP potential one only requires the dielectric response of the surface at the resonance transition frequency ǫ m ≡ ǫ(ω m ) (assuming µ(ω m ) = 1).…”

“…However, an analog of the Earnshaw's theorem for fluctuation forces forbids stable equilibria for non-magnetic objects separated by vacuum [34]. Some possible ways to overcome this no-go theorem are [35]: going out-ofequilibrium using temperature gradients [36][37][38] or external drives [40], replacing the vacuum by a medium with appropriate permittivity relative to the interacting objects [41][42][43], using material anisotropies [44][45][46] and topological properties of the interacting bodies [47,48], or designing specific geometrical configurations [49].…”